Classroom conundrum

In a class, every boy is a friend of exactly three girls and every girl is a friend of exactly two boys . The room only has 19 tables (which can be used by two students maximum) and 31 students in this class are studying French. How many students have this class?

#NumberTheory

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

The ratio of boys to girls must be $2:3,$ i.e., there will be $2n$ boys and $3n$ girls for some integer $n.$ Thus there will be $2n + 3n = 5n$ students, so we are looking for a multiple of $5$ between $31$ and $38.$ The only such integer is $5*7 = 35,$ so there are $35$ students, $14$ of whom are boys and $21$ of whom are girls.

Brian Charlesworth - 5 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$